The present invention relates to a light modulator for representing complex-valued information, comprising an encoding surface with an arrangement of pixels whose transmissive or reflective phase shift is controllable.
The computation of computer-generated holograms and similar diffractive structures for encoding on pixelated light modulators generally provides complex-valued information, i.e. numbers, with a real part and an imaginary part, said information being written in the form of amplitude or phase information to the light modulator with a discrete pixel structure and being reconstructed with the help of sufficiently coherent illumination.
The light modulators typically only allow the amplitude or phase information to be written to a pixel, but disallow the entire complex number, i.e. any combination of amplitude and phase information to be written simultaneously.
Known methods to solve this problem, as for example described in document U.S. Pat. No. 5,416,618, use either a combination of multiple light modulators, for example an amplitude-modulating light modulator and a phase-modulating light modulator, or two amplitude-modulating or phase-modulating light modulators so to be able to represent a complex number in each pixel. However, this has the disadvantage that a difficult adjustment is required because the pixel structure of the two light modulators must be congruent.
This disadvantage will be irrelevant if a complex number is represented by a group of multiple pixels on the same light modulator. However, this involves complicated encoding methods which are associated with an iterative computation of the complex-valued code.
One possibility of applying these encoding methods is to use multiple phase values, in particular to use a two-phase encoding method. A complex number here is represented by a sum of two numbers with same absolute value and different phase values and is written to two adjacent pixels of the same light modulator.
The interference of coherent light which passes through both pixels then shows the same effect as light which passed through a single complex-valued pixel. However, this only applies if there is no further optical retardation except the computed one of the light beams between the two pixels.
However, on the one hand, if light is diffracted at the adjacent pixels of a pixel group then an angle-specific optical retardation occurs, which causes errors in the hologram reconstruction.
On the other hand, the angle-specific optical retardation between a group of pixels which represents a complex number, relative to adjacent groups of pixels which represent other complex numbers, is essential for hologram reconstruction, because this is what represents the principle of diffraction, on which the hologram reconstruction is based.
Document DE 10 2006 003 741.3 describes for a two-phase encoding method a modification of the hologram computation with the help of an iterative method, whereby an improvement of the reconstruction is achieved. However, this causes an increased computational load, which is for example disturbing in a real-time computation of holograms.
Due to pixel dimensions of conventional light modulators, another problem in display holography is the very small useable diffraction angle, which greatly limits either the extent or the visibility region of a holographically reconstructed scene. Now, if multiple adjacent pixels are used for encoding complex hologram values, the diffraction angle will be further reduced. This disadvantage is not compensated by avoiding the vertical parallax to be encoded, i.e. if only the horizontal parallax is holographically encoded.
Document U.S. Pat. No. 3,633,989, for example, describes a method of display holography involving one-dimensionally encoded holograms, where a hologram is for example only encoded horizontally (horizontal-parallax-only holograms—HPO). Values for the hologram are computed independently of each other and are typically written to individual rows of a light modulator.
A specific device for reconstructing one-dimensional holograms is created when using a light modulator with a one-dimensional arrangement of pixels. A spatial scene can then for example be reconstructed in that individual rows of a hologram are displayed sequentially on the light modulator and are strung together in the vertical direction in combination with a scanning unit.
If an HPO encoding method and a light modulator with a two-dimensional arrangement of pixels are used, and if there are no mutually independent values which are written to each row of the light modulator, but always groups of multiple rows, there will be the possibility to widen the usable horizontal diffraction angle at the cost of a loss of vertical resolution. A particular possibility is the coherent combination of multiple hologram rows. With a two-phase encoding method, the two phase values can for example be written to two adjacent rows of the light modulator. However, a coherent illumination of the respective groups of rows will then also be necessary for the reconstruction.
In HPO holograms, a dependence of the hologram reconstruction on the vertical diffraction angle is not desired. However, if a group of rows of a light modulator is coherently illuminated, this will cause in the vertical direction an undesired, angle-specific retardation among the individual rows, while in the horizontal direction the retardation among adjacent columns is required for the reconstruction, because in a phase encoding method it comprises the information about the object to be reconstructed.
In either case, for the phase encoding method with multiple pixels for representing a complex number, and for the coherent combination of multiple HPO-encoded light modulator rows, the same problem occurs: on the one hand, a disturbing, angle-specific optical retardation occurs between the groups of few adjacent pixels, while on the other hand the optical retardation to other pixels or pixel groups, which is likewise generated, is either insignificant or even required for the hologram reconstruction.